The table shows a bacterial population y after x days


days, X 0,1,2,3,4

Population,8,24,72,216,648


Write an exponential function that represents the population


Y=

Zachary expects to make $40 + $7 x tt (number of tables) in a day when waiting on tt tables

If Zachary waits on 11 tables, he can expect to make an additional $7 in tips for each table, for a total of 11 tables * $7/table = $77 in tips.

When added to his guaranteed wage, Zachary can expect to earn $40 (guaranteed wage) + $77 (tips) = $117 for that day.

To calculate how much Zachary would expect to make in a day when waiting on tt tables, we can use the equation:

Earnings = $40 (guaranteed wage) + $7 (tips/table) x tt (number of tables)

So if tt represents the number of tables Zachary waits on, then he can expect to earn:

Earnings = $40 + $7 x tt

For example, if Zachary waits on 15 tables, he can expect to earn $40 + $7 x 15 = $190.

Zachary can use this equation to calculate his expected earnings for any number of tables he waits on in a day.

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Answer:

cos(2x)

Step-by-step explanation:

To simplify the expression cos²x - sin²x, we can use the identity cos²x - sin²x = cos(2x).

This identity can be derived by using the double angle formula for cosine:

cos(2x) = cos(x + x) = cos(x)cos(x) - sin(x)sin(x) = cos²x - sin²x

Therefore, the expression cos²x - sin²x can be simplified to cos(2x).

Answer:

--------------------------

Let the cost of a hotdog be h and pretzel be p.

Set up equations as per question:

Divide the second equation by 2, then subtract from the first one:

Now find the value of p:

Hotdog costs $2 and pretzel costs $0.75.

Answer:3/4 is the answer

Step-by-step explanation:

Answer:(s)

1/4  -  7/1  =  - 27/4  

Decimal:   - 6.75

Mixed number:  - 6 3/4

Step-by-step explanation:

1/4  -  7/1  =  - 27/4  or - 6.75 or  - 6 3/4

LCM:   4, 1  = 4

Adjust Fraction Based On LCM:

1/4 - 28/4

Apply The Fraction Rule:

a/c - b/c  =  a - b/c

1 - 28/4

Subtract the numbers:

1  -  28   =  - 27

             =  -27/4

Apply Fraction Rule:

- a/b  =  - a/b

Thus:

1/4 - 7/1  =  - 27/4  

Decimal:   - 6.75

Mixed Number Form  - 6 3/4

I hope that helps you!!!

If a  box of 6 donuts has 3 plain donuts, 2 chocolate donuts, and 1 blueberry donut. The number of  visually distinct arrangements of the donuts that are there is: 60.

Using this formula to find the  number of  visually distinct arrangements of the donut that are there.

Number  visually distinct arrangements = Box of  donuts!/ Plain donuts! × Chocolate donuts! × Blueberry donut!

Let plug in the formula

Number  visually distinct arrangements = 6!/ 3! × 2! × 1!

Number  visually distinct arrangements = 720/ 6 ×2 × 1

Number  visually distinct arrangements = 720 /12

Number  visually distinct arrangements = 60

Therefore the number of Number  visually distinct arrangements  is 12.

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The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.

In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.

A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.

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The total cost of Jess Norton is $995.85 and the total cost of Olive Baker is $678 .

What is total cost ?

The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost = (Average Fixed Cost x Average Variable Cost) x Units Produced is the formula.

In economics, total cost is the total of all expenses a company incurs to produce a particular level of output.

The average cost, or the typical sum of money required to create a unit, can be determined using the cost function. The average cost function is A(x)=C(x)x, where x > 0 and C is the constant. Calculating the average cost per unit requires dividing the total cost by the quantity of units produced.

 2 one hundred dollar bills = 2 x $100

                                                   = $200                

 Total deposits = 2 one hundred dollar bills + Checks

                                = $200 + $474.85 + $321

                                = $995.85          

 Checks amount = $100 x 4

                                   = $400                  

 12 for $7.5

       = 12 x $7.5

       = $90                  

 Six 20-dollar bills = 6 x $20

                                     = $120                  

 Five 10-dollar bills = 5 x $10

                                      = $50                  

 Eighteen 1-dollar bills = 18 x $1

                                            = $18                

 Total deposits = $400 + $90 + $120 + $50 + $18

                                = $678

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Answer: B

Step-by-step explanation:

B) 180−m180-m180−m

On solving the provided question, we can say that the quadratic equation is  y = 5x² - 9x + 3 this quadratic equation can not factorized further

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is

y = 5x² - 9x + 3

this quadratic equation can not factorized further

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In positive exponents, the simplified form of the above polynomial is s⁷/t¹¹.

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here,

=4s⁵*t⁻⁷/-2s⁻²*-2t⁴

=s⁷/t¹¹

The simplified form of given polynomial is s⁷/t¹¹ in positive exponents.

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A one million sided shape called as Megagon.

We know that a polygon is noting but a closed two-dimensional figure which is enclosed by line segments.

These line segments are known as sides.

A polygon has at least three straight sides and angles.

Polygons are classified mainly into four categories. Regular polygon, Irregular polygon, Convex polygon and Concave polygon

We know that a polygon with n sides is called n-gon.

For n = 1000000, i.e., a polygon with one million sides is called as Megagon.

A number of edges and vertices = 1000000

And the internal angle of megagon is about 179.99 degrees.

Therefore, a shape with  1 million sides is known as a Megagon

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Answer:

x=7/2

x=3/2

Step-by-step explanation:

Answer: ax^2+bx+c=0

(4x^2+20x+20=0)

Step-by-step explanation:

It may not make sense but...

Add -20 to both sides of the equation.

4x-20x=-20

Add -20 to both sides of the equation.

4x^2-20x+20=-20+20

Simplify the expression.

4x^2+20x+20=0

I hope this was what you were looking for. :) If not I'm still glad to help.

Answer:

5pie/6,0

Step-by-step explanation:

i graphed it

Answer:

yes, it uses the Associative Property

Step-by-step explanation:

The two expressions (8 + 27) + 52 and 8 + (27 + 52) are equivalent because they both equal 87. This is an example of the Associative Property of Addition which states that the order of the terms within an expression can be changed without changing the result.

Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

The smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

To compute this, first convert 5 to binary and base-4:

5 in binary: 101

5 in base-4: 11

Since 11 is the same in both bases, the next number that would be a palindrome in both bases is 11.

To find the base 10 number of this palindrome, we convert 11 from binary and base-4 to base 10:

11 in binary: 1011

11 in base-4: 111

Therefore, the smallest base-10 positive integer greater than 5 that is a palindrome when written in both base 2 and 4 is 11.

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Consequently, this student's quiz results have a median, or "middle," value of 16.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.

Exam results:

9, 13, 20, 15, 18, 17

Number the rows and columns.

9, 13, 15, 17, 18, 20

Calculate the "middle" value:

9, 13, 15, 17, 18, 20

If there are two middle values, put them together and divide by two.

15 + 17 = 32

32/2 = 16

Consequently, this student's quiz results have a median, or "middle," value of 16.

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Option D) f(x) = |x|, is Correct.

What is parent function?

A parent function is a basic or fundamental function that serves as the starting point for a family or group of related functions. These functions can be obtained by applying a transformation to the parent function, such as shifting, stretching, or reflecting it.

The absolute value parent function is represented by the following function:

D. f(x) = |x|

The absolute value function is defined as |x| = x for x >= 0 and |x| = -x for x < 0. Graph of this function is a V-shape, and it's also known as "the absolute value of x" function. It is a reflection of the linear function f(x) = x across the x-axis and will always have a slope of 1 and a y-intercept of 0.

A. f(x) = x is a linear function, slope is 1 and y-intercept is 0, This is not absolute value function

B. f(x) = 2ˣ is the exponential function, and it is not an absolute value function

C. f(x) = x² is the quadratic function, it's a parabola opening upwards and not an absolute value function

D. f(x) = |x| is the absolute value function, V-shape and it's an example of the absolute value parent function.

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Answer:

The answer is Terrestrial planets

4 is the additive inverse of -4.

              OR

The opposite of 4 is -4, or negative four.

Now, According to the question:

Opposite numbers:-

Every number has an opposite. In fact, every number has two opposites: the additive inverse and the reciprocal—or multiplicative inverse. Don't be intimidated by these technical-sounding names, though. Finding a number's opposites is actually pretty straightforward.

If a number is added to its additive inverse, the sum of both the numbers becomes zero.

For any given number, the additive inverse is a number or a value which when added to the original number results in zero.

Mathematically: a + (-a) = 0

So here, 'a' and '-a' are the additive inverses of each other.

Therefore, for 4, the additive inverse is 4 = -4

Thus, 4 is the additive inverse of -4.

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The horizontal line of the graph is known as x axis,

The term graph in math is defined as the visual representation of data or the function in math.

Here we have to find the definition for the horizontal line on a graph.

Here we know that the straight line that is mapped from left to right and it is parallel to the X-axis in the plane coordinate system.

On the other hand, we all also know that the straight line that does not make any intercept on the X-axis and it can have an intercept on Y-axis is called horizontal line.

And we all also know that the straight line that is parallel to the x-axis and where all the points on the line have the same y-coordinate and basically all horizontal lines are parallel to each other.

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The Value of the two constants K and R are 5 and 3 respectively.

a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:

u2 = 2u1 + 20 = 2(8) + 20 = 36

So u2 = 36.

b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:

Substituting in the given values:

Solving for r and k, we get:

k = 5 and r = 3.

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If 1 gallon equals 4 quarts, Lorraine fill can 4 jars. Hence option B is the correct option.

What is the unit of an object?

The user can describe locations and dimensions in a wide range of various coordinate systems using unit objects. Every drawing is done in relation to a viewport, and the units determine the coordinate system to use there. "npc" is one example of a unit (coordinate system).

Given Lorraine filled a pot with tomatoes and the volume of the pot is 1.5 gallons.

She wants to fill the tomatoes in jars. The volume of the jar is  1.5 quarts.

1 gallon is equal to 4 quarts.

1.5 gallons is equal to 1.5 × 4 quarts = 6 quarts.

The number of jars that are filled with tomatoes is 6 quarts/ 1.5 quarts = 4.

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The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by

y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].

To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is

1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is

-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.

1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]

=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].

When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.

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Answer: t = 0

Step-by-step explanation:

Expand 8950×0.7²: 4385.5t

8950(0.7) ²t

8950×0.49t = 4385.5t

N(t) = 4385.5t

N(t) - 4385.5t=0

Factor N(t) - 4385.5t: t (N - 4385.5)

t (N - 4385.5) =0

t=0

On [0,∞] the function grows, whereas on [-∞, 0], it shrinks. f has absolute minimum value is 0, and it also has the same relative minimum value (0,0).

On the graph, you are able to see a "open circle" at it when x< 0. (0, 0).

There consequently no absolute maximum value of f due to the graph's infinitely high y values.

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The circle's radius is equal to 3.659 or 3.7.

A circle's or a sphere's radius is the length of the line between the center and the edge.

From the center of the circle or sphere to any point on its perimeter, the radius' length is constant.

Its diameter is halved by its length.

A line segment from a circle's or sphere's center to its perimeter or boundary is known as the radius in geometry. I

t is a crucial component of spheres and circles and is frequently abbreviated as "r."

When discussing multiple radiuses at once, the plural form of radius is "radii." the longest line connecting any points on the opposite side of a circle or sphere.

Hence, The circle's radius is equal to 3.659 or 3.7.

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Answer:

C:  (-8, 2)

Step-by-step explanation:

Given parabola:

[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]

For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.  

Therefore, the x-value of the vertex of the given parabola is:

[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]

To find the y-value of the vertex, input x = -8 into the given equation:

[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]

Therefore, the vertex (h, k) of the parabola is (-8, 4).

The focus of the parabola is (h, k+p) where:

Therefore:

[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]

Answer:

$8.

Step-by-step explanation:

right!!

The process to find the asymptote and zeros of the function is explained below.

The term asymptote is referred as a horizontal/vertical/slant line to which the curve is very close to but the curve doesn't touch the asymptote.

Here we need to find the way to identify the asymptotes and zeros of a function.

The process of finding the asymptote is defined as,

If you want to find the horizontal asymptotes, then apply the limit x→∞ or x→ -∞.

Where as if you want to find the vertical asymptotes, then apply the limit y→∞ or y→ -∞.

Finally, if you want to find the slant asymptote, then divide the numerator by the denominator.

The process of finding the zero of the function is defined as the way to find the values of x where f(x) = 0.

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